(CNN) — A referendum that would constitutionally ban same-sex marriages in North Carolina is in the spotlight Tuesday, as three states hold primaries.

Amendment One would alter North Carolina’s constitution to say that “marriage between one man and one woman is the only domestic legal union that shall be valid or recognized in this State.”

Supporters say the amendment is needed to stop those whom they say are trying to redefine marriage.

Opponents say the measure is unnecessary since the state already has a law in place that bans same-sex marriages and that it could jeopardize domestic violence protections for women and affect health benefits for same-sex couples.

The bill proposing the amendment says only a simple majority is needed for the amendment to pass. Some 500,000 people have already cast ballots on the measure through early voting or absentee ballots.

Some high-profile surrogates have come out on both sides of the measure.

Evangelist Billy Graham endorsed the ballot initiative, a rare move for a preacher who has typically avoided political fights. Graham took out full-page ads in 14 North Carolina newspapers touting his support for the measure, saying “the Bible is clear — God’s definition of marriage is between a man and a woman.”

Graham’s website encourages churches to download a poster that bears his image and the message “Vote for Marriage May 8th.”

On the other side, former President Bill Clinton opposed the amendment in a taped recording sent by phone to hundreds of thousands of North Carolina homes.

“So the real effect of the law is not to keep the traditional definition of marriage, you’ve already done that,” Clinton says in the recording. “The real effect of the law will be to hurt families and drive away jobs. North Carolina can do better.”

The only recent public opinion polling on the issue, from a group that does work for Democratic candidates and causes, indicates that a majority of North Carolina voters support the amendment.

Indiana and West Virginia also hold primaries on Tuesday.

In Indiana, the Senate’s longest-serving Republican may not survive a primary challenge — the most recent public opinion poll indicates Sen. Dick Lugar trailing his primary challenger, state Treasurer Richard Mourdock, by double digits.

Lugar, who is serving his sixth term in the Senate, has been forced to defend his residency in the state, as well as his conservative credentials, against Mourdock, who enjoys strong support from many in the tea party movement.